Welcome to the forum. That's a nice old gun in seemingly pretty good shape, but the frame edges under the barrel look just a little rounded to me. This may have been a blued gun to start with that was later refinished in nickel. Can we see a photo of the other side of it? Is there a five-pointed star pounded into the frame anywhere near the serial number? The star can sometimes indicated factory refinishing, but the absence of a star can't be taken to mean that the gun has not been refinished.
That gun probably dates from 1910-11. It is an example of the .38 Hand Ejector Military & Police Third Model. If you want to get really precise, collectors would recognize it as the third model, third change; that recognizes some engineering and design changes made in the M&P line as the gun, which was introduced in 1899, evolved over about 15 years into the design that it held for much of the 20th century. The .38 Special M&P was S&W's most successful gun; they made millions of them.
It's safe to shoot modern .38 special ammunition as long as you stay away from the hot-loaded rounds and the +P ammo. I have an old M&P from 1904 that I shoot with wadcutter target ammo.
The earliest M&P revolvers were round butt guns, but the square butt option was introduced in 1905. Most prewar and wartime M&Ps square butt guns, so you have one of the less common varieties (not that being less common makes it rare).
